What is the d/(dt)((h(t))(4t+10)) ?

The d/(dt)((h(t))(4t+10)) is h(8t+10)

What is the first d/(dt)((h(t))(4t+10)) ?

The first d/(dt)((h(t))(4t+10)) is h(8t+10)

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\frac{d}{d t} ((h (t)) (4 t + 10))

h (8 t + 10)

Solution steps

\frac{d}{d t} ((h (t)) (4 t + 10))

Treat

h

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= h \frac{d}{d t} (t (4 t + 10))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = 4 t + 10

= h (\frac{d t}{d t} (4 t + 10) + \frac{d}{d t} (4 t + 10) t)

\frac{d t}{d t} = 1

\frac{d}{d t} (4 t + 10) = 4

= h (1 \cdot (4 t + 10) + 4 t)

Simplify

= h (8 t + 10)

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What is the d/(dt)((h(t))(4t+10)) ?
The d/(dt)((h(t))(4t+10)) is h(8t+10)
What is the first d/(dt)((h(t))(4t+10)) ?
The first d/(dt)((h(t))(4t+10)) is h(8t+10)